---
name: "sqpt01.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/sqpt01.f"
---

# sqpt01.f(3)

## NAME

TESTING/LIN/sqpt01.f

## SYNOPSIS

### Functions/Subroutines

real function **sqpt01** (m, n, k, a, af, lda, tau, jpvt, work, lwork)\
 **SQPT01**

## Function/Subroutine Documentation

### real function sqpt01 (integer m, integer n, integer k, real, dimension( lda, \* ) a, real, dimension( lda, \* ) af, integer lda, real, dimension( \* ) tau, integer, dimension( \* ) jpvt, real, dimension( lwork ) work, integer lwork)

**SQPT01**

**Purpose:**

```
!>
!> SQPT01 tests the QR-factorization with pivoting of a matrix A.  The
!> array AF contains the (possibly partial) QR-factorization of A, where
!> the upper triangle of AF(1:k,1:k) is a partial triangular factor,
!> the entries below the diagonal in the first k columns are the
!> Householder vectors, and the rest of AF contains a partially updated
!> matrix.
!>
!> This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )
!> where || . || is matrix one norm.
!>
```

**Parameters**

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrices A and AF.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrices A and AF.
!>
```

*K*

```
!>          K is INTEGER
!>          The number of columns of AF that have been reduced
!>          to upper triangular form.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA, N)
!>          The original matrix A.
!>
```

*AF*

```
!>          AF is REAL array, dimension (LDA,N)
!>          The (possibly partial) output of SGEQPF.  The upper triangle
!>          of AF(1:k,1:k) is a partial triangular factor, the entries
!>          below the diagonal in the first k columns are the Householder
!>          vectors, and the rest of AF contains a partially updated
!>          matrix.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the arrays A and AF.
!>
```

*TAU*

```
!>          TAU is REAL array, dimension (K)
!>          Details of the Householder transformations as returned by
!>          SGEQPF.
!>
```

*JPVT*

```
!>          JPVT is INTEGER array, dimension (N)
!>          Pivot information as returned by SGEQPF.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of the array WORK.  LWORK >= M*N+N.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **119** of file **sqpt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.